Is this relation on $A$ transitive? I know that the relation is reflexive and symmetric but I can not tell if it's transitive.
$\mathcal R =\{(a,a), (a,b), (a,c), (b,a), (b,b), (b,d), (c,a), (c,c), (c,d), (d,b), (d,c), (d,d)\}$
where $A = \{a,b,c,d\}$
No is is not, $a \mathcal R b$ and $b \mathcal R d$ but $a \mathcal \not R d$